arcball.h

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#pragma once
 
// 8<--Snip here if you have your own math types/funcs-->8 
 
# include <assert.h>
 
//Math types derived from the KempoApi tMath library
typedef union {
    struct {
        float X, Y;
    } s;
 
    float T[2];
} Tuple2fT;                     //A generic 2-element tuple that is represented by single-precision floating point x,y coordinates. 
 
typedef union {
    struct {
        float X, Y, Z;
    } s;
 
    float T[3];
} Tuple3fT;                     //A generic 3-element tuple that is represented by single precision-floating point x,y,z coordinates. 
 
typedef union {
    struct {
        float X, Y, Z, W;
    } s;
 
    float T[4];
} Tuple4fT;                     //A 4-element tuple represented by single-precision floating point x,y,z,w coordinates. 
 
typedef union {
    float M[9];
    struct {
        //column major
        union {
            float M00;
            float XX;
            float SX;
        };                      //XAxis.X and Scale X
        union {
            float M10;
            float XY;
        };                      //XAxis.Y
        union {
            float M20;
            float XZ;
        };                      //XAxis.Z
        union {
            float M01;
            float YX;
        };                      //YAxis.X
        union {
            float M11;
            float YY;
            float SY;
        };                      //YAxis.Y and Scale Y
        union {
            float M21;
            float YZ;
        };                      //YAxis.Z
        union {
            float M02;
            float ZX;
        };                      //ZAxis.X
        union {
            float M12;
            float ZY;
        };                      //ZAxis.Y
        union {
            float M22;
            float ZZ;
            float SZ;
        };                      //ZAxis.Z and Scale Z
    } s;
} Matrix3fT;                    //A single precision floating point 3 by 3 matrix. 
 
typedef union {
    float M[16];
    struct {
        //column major
        union {
            float M00;
            float XX;
            float SX;
        };                      //XAxis.X and Scale X
        union {
            float M10;
            float XY;
        };                      //XAxis.Y
        union {
            float M20;
            float XZ;
        };                      //XAxis.Z
        union {
            float M30;
            float XW;
        };                      //XAxis.W
        union {
            float M01;
            float YX;
        };                      //YAxis.X
        union {
            float M11;
            float YY;
            float SY;
        };                      //YAxis.Y and Scale Y
        union {
            float M21;
            float YZ;
        };                      //YAxis.Z
        union {
            float M31;
            float YW;
        };                      //YAxis.W
        union {
            float M02;
            float ZX;
        };                      //ZAxis.X
        union {
            float M12;
            float ZY;
        };                      //ZAxis.Y
        union {
            float M22;
            float ZZ;
            float SZ;
        };                      //ZAxis.Z and Scale Z
        union {
            float M32;
            float ZW;
        };                      //ZAxis.W
        union {
            float M03;
            float TX;
        };                      //Trans.X
        union {
            float M13;
            float TY;
        };                      //Trans.Y
        union {
            float M23;
            float TZ;
        };                      //Trans.Z
        union {
            float M33;
            float TW;
            float SW;
        };                      //Trans.W and Scale W
    } s;
} Matrix4fT;                    //A single precision floating point 4 by 4 matrix. 
 
 
//"Inherited" types
#define Point2fT    Tuple2fT    //A 2 element point that is represented by single precision floating point x,y coordinates.
 
#define Quat4fT     Tuple4fT    //A 4 element unit quaternion represented by single precision floating point x,y,z,w coordinates.
 
#define Vector3fT   Tuple3fT    //A 3-element vector that is represented by single-precision floating point x,y,z coordinates.
 
//Custom math, or speed overrides
#define FuncSqrt    sqrtf
 
//utility macros
//assuming IEEE-754(float), which i believe has max precision of 7 bits
# define Epsilon 1.0e-5
 
//Math functions
 
#ifdef ARCBALL_C
static void Vector3fCross(Vector3fT * NewObj, const Vector3fT * v1,
                          const Vector3fT * v2)
{
    Vector3fT Result;           //safe not to initialize
 
    assert(NewObj && v1 && v2);
 
    // store on stack once for aliasing-safty
    // i.e. safe when a.cross(a, b)
 
    Result.s.X = (v1->s.Y * v2->s.Z) - (v1->s.Z * v2->s.Y);
    Result.s.Y = (v1->s.Z * v2->s.X) - (v1->s.X * v2->s.Z);
    Result.s.Z = (v1->s.X * v2->s.Y) - (v1->s.Y * v2->s.X);
 
    //copy result back
    *NewObj = Result;
}
 
static float Vector3fDot(const Vector3fT * NewObj, const Vector3fT * v1)
{
    assert(NewObj && v1);
 
    return (NewObj->s.X * v1->s.X) +
        (NewObj->s.Y * v1->s.Y) + (NewObj->s.Z * v1->s.Z);
}
 
static float Vector3fLengthSquared(const Vector3fT * NewObj)
{
    assert(NewObj);
 
    return (NewObj->s.X * NewObj->s.X) +
        (NewObj->s.Y * NewObj->s.Y) + (NewObj->s.Z * NewObj->s.Z);
}
 
static float Vector3fLength(const Vector3fT * NewObj)
{
    assert(NewObj);
 
    return FuncSqrt(Vector3fLengthSquared(NewObj));
}
 
    //$hack this can be optimized some(if s == 0)
 
static void Matrix3fSetRotationFromQuat4f(Matrix3fT * NewObj,
                                          const Quat4fT * q1)
{
    float n, s;
    float xs, ys, zs;
    float wx, wy, wz;
    float xx, xy, xz;
    float yy, yz, zz;
 
    assert(NewObj && q1);
 
    n = (q1->s.X * q1->s.X) + (q1->s.Y * q1->s.Y) + (q1->s.Z * q1->s.Z) +
        (q1->s.W * q1->s.W);
    s = (n > 0.0f) ? (2.0f / n) : 0.0f;
 
    xs = q1->s.X * s;
    ys = q1->s.Y * s;
    zs = q1->s.Z * s;
    wx = q1->s.W * xs;
    wy = q1->s.W * ys;
    wz = q1->s.W * zs;
    xx = q1->s.X * xs;
    xy = q1->s.X * ys;
    xz = q1->s.X * zs;
    yy = q1->s.Y * ys;
    yz = q1->s.Y * zs;
    zz = q1->s.Z * zs;
 
    NewObj->s.XX = 1.0f - (yy + zz);
    NewObj->s.YX = xy - wz;
    NewObj->s.ZX = xz + wy;
    NewObj->s.XY = xy + wz;
    NewObj->s.YY = 1.0f - (xx + zz);
    NewObj->s.ZY = yz - wx;
    NewObj->s.XZ = xz - wy;
    NewObj->s.YZ = yz + wx;
    NewObj->s.ZZ = 1.0f - (xx + yy);
}
 
static void Matrix3fMulMatrix3f(Matrix3fT * NewObj, const Matrix3fT * m1)
{
    Matrix3fT Result;           //safe not to initialize
 
    assert(NewObj && m1);
 
    // alias-safe way.
    Result.s.M00 =
        (NewObj->s.M00 * m1->s.M00) + (NewObj->s.M01 * m1->s.M10) +
        (NewObj->s.M02 * m1->s.M20);
    Result.s.M01 =
        (NewObj->s.M00 * m1->s.M01) + (NewObj->s.M01 * m1->s.M11) +
        (NewObj->s.M02 * m1->s.M21);
    Result.s.M02 =
        (NewObj->s.M00 * m1->s.M02) + (NewObj->s.M01 * m1->s.M12) +
        (NewObj->s.M02 * m1->s.M22);
 
    Result.s.M10 =
        (NewObj->s.M10 * m1->s.M00) + (NewObj->s.M11 * m1->s.M10) +
        (NewObj->s.M12 * m1->s.M20);
    Result.s.M11 =
        (NewObj->s.M10 * m1->s.M01) + (NewObj->s.M11 * m1->s.M11) +
        (NewObj->s.M12 * m1->s.M21);
    Result.s.M12 =
        (NewObj->s.M10 * m1->s.M02) + (NewObj->s.M11 * m1->s.M12) +
        (NewObj->s.M12 * m1->s.M22);
 
    Result.s.M20 =
        (NewObj->s.M20 * m1->s.M00) + (NewObj->s.M21 * m1->s.M10) +
        (NewObj->s.M22 * m1->s.M20);
    Result.s.M21 =
        (NewObj->s.M20 * m1->s.M01) + (NewObj->s.M21 * m1->s.M11) +
        (NewObj->s.M22 * m1->s.M21);
    Result.s.M22 =
        (NewObj->s.M20 * m1->s.M02) + (NewObj->s.M21 * m1->s.M12) +
        (NewObj->s.M22 * m1->s.M22);
 
    //copy result back to this
    *NewObj = Result;
}
 
 
static void Matrix4fSetRotationScaleFromMatrix4f(Matrix4fT * NewObj,
                                                 const Matrix4fT * m1)
{
    assert(NewObj && m1);
 
    NewObj->s.XX = m1->s.XX;
    NewObj->s.YX = m1->s.YX;
    NewObj->s.ZX = m1->s.ZX;
    NewObj->s.XY = m1->s.XY;
    NewObj->s.YY = m1->s.YY;
    NewObj->s.ZY = m1->s.ZY;
    NewObj->s.XZ = m1->s.XZ;
    NewObj->s.YZ = m1->s.YZ;
    NewObj->s.ZZ = m1->s.ZZ;
}
 
static float Matrix4fSVD(const Matrix4fT * NewObj, Matrix3fT * rot3,
                           Matrix4fT * rot4)
{
    float s, n;
 
    assert(NewObj);
 
    // this is a simple svd.
    // Not complete but fast and reasonable.
    // See comment in Matrix3d.
 
    s = FuncSqrt(((NewObj->s.XX * NewObj->s.XX) +
                  (NewObj->s.XY * NewObj->s.XY) +
                  (NewObj->s.XZ * NewObj->s.XZ) +
                  (NewObj->s.YX * NewObj->s.YX) +
                  (NewObj->s.YY * NewObj->s.YY) +
                  (NewObj->s.YZ * NewObj->s.YZ) +
                  (NewObj->s.ZX * NewObj->s.ZX) +
                  (NewObj->s.ZY * NewObj->s.ZY) +
                  (NewObj->s.ZZ * NewObj->s.ZZ)) / 3.0f);
 
    if (rot3)                   //if pointer not null
    {
        rot3->s.XX = NewObj->s.XX;
        rot3->s.XY = NewObj->s.XY;
        rot3->s.XZ = NewObj->s.XZ;
        rot3->s.YX = NewObj->s.YX;
        rot3->s.YY = NewObj->s.YY;
        rot3->s.YZ = NewObj->s.YZ;
        rot3->s.ZX = NewObj->s.ZX;
        rot3->s.ZY = NewObj->s.ZY;
        rot3->s.ZZ = NewObj->s.ZZ;
 
        // zero-div may occur.
 
        n = 1.0f / FuncSqrt((NewObj->s.XX * NewObj->s.XX) +
                            (NewObj->s.XY * NewObj->s.XY) +
                            (NewObj->s.XZ * NewObj->s.XZ));
        rot3->s.XX *= n;
        rot3->s.XY *= n;
        rot3->s.XZ *= n;
 
        n = 1.0f / FuncSqrt((NewObj->s.YX * NewObj->s.YX) +
                            (NewObj->s.YY * NewObj->s.YY) +
                            (NewObj->s.YZ * NewObj->s.YZ));
        rot3->s.YX *= n;
        rot3->s.YY *= n;
        rot3->s.YZ *= n;
 
        n = 1.0f / FuncSqrt((NewObj->s.ZX * NewObj->s.ZX) +
                            (NewObj->s.ZY * NewObj->s.ZY) +
                            (NewObj->s.ZZ * NewObj->s.ZZ));
        rot3->s.ZX *= n;
        rot3->s.ZY *= n;
        rot3->s.ZZ *= n;
    }
 
    if (rot4)                   //if pointer not null
    {
        if (rot4 != NewObj) {
            Matrix4fSetRotationScaleFromMatrix4f(rot4, NewObj); // private method
        }
        // zero-div may occur.
 
        n = 1.0f / FuncSqrt((NewObj->s.XX * NewObj->s.XX) +
                            (NewObj->s.XY * NewObj->s.XY) +
                            (NewObj->s.XZ * NewObj->s.XZ));
        rot4->s.XX *= n;
        rot4->s.XY *= n;
        rot4->s.XZ *= n;
 
        n = 1.0f / FuncSqrt((NewObj->s.YX * NewObj->s.YX) +
                            (NewObj->s.YY * NewObj->s.YY) +
                            (NewObj->s.YZ * NewObj->s.YZ));
        rot4->s.YX *= n;
        rot4->s.YY *= n;
        rot4->s.YZ *= n;
 
        n = 1.0f / FuncSqrt((NewObj->s.ZX * NewObj->s.ZX) +
                            (NewObj->s.ZY * NewObj->s.ZY) +
                            (NewObj->s.ZZ * NewObj->s.ZZ));
        rot4->s.ZX *= n;
        rot4->s.ZY *= n;
        rot4->s.ZZ *= n;
    }
 
    return s;
}
 
 
static void Matrix4fSetRotationScaleFromMatrix3f(Matrix4fT * NewObj,
                                                 const Matrix3fT * m1)
{
    assert(NewObj && m1);
 
    NewObj->s.XX = m1->s.XX;
    NewObj->s.YX = m1->s.YX;
    NewObj->s.ZX = m1->s.ZX;
    NewObj->s.XY = m1->s.XY;
    NewObj->s.YY = m1->s.YY;
    NewObj->s.ZY = m1->s.ZY;
    NewObj->s.XZ = m1->s.XZ;
    NewObj->s.YZ = m1->s.YZ;
    NewObj->s.ZZ = m1->s.ZZ;
}
 
 
static void Matrix4fMulRotationScale(Matrix4fT * NewObj, float scale)
{
    assert(NewObj);
 
    NewObj->s.XX *= scale;
    NewObj->s.YX *= scale;
    NewObj->s.ZX *= scale;
    NewObj->s.XY *= scale;
    NewObj->s.YY *= scale;
    NewObj->s.ZY *= scale;
    NewObj->s.XZ *= scale;
    NewObj->s.YZ *= scale;
    NewObj->s.ZZ *= scale;
}
 
static void Matrix4fSetRotationFromMatrix3f(Matrix4fT * NewObj,
                                            const Matrix3fT * m1)
{
    float scale;
 
    assert(NewObj && m1);
 
    scale = Matrix4fSVD(NewObj, NULL, NULL);
 
    Matrix4fSetRotationScaleFromMatrix3f(NewObj, m1);
    Matrix4fMulRotationScale(NewObj, scale);
}
#endif
 
// 8<--Snip here if you have your own math types/funcs-->8 
struct _ArcBall_t {
    Vector3fT StVec;
    Vector3fT EnVec;
    float AdjustWidth;
    float AdjustHeight;
    Matrix4fT Transform;
    Matrix3fT LastRot;
    Matrix3fT ThisRot;
    Point2fT MousePt;
    int isClicked;
    int isRClicked;
    int isDragging;
};
 
 
void init_arcBall(ArcBall_t * a, float NewWidth, float NewHeight);
void arcmouseClick(void);
void arcmouseDrag(void);